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課程名稱 |
數值偏微分方程式二
Numerical Partial Differential Equations (Ⅱ) |
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開課學期 |
100-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
薛克民 |
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課號 |
MATH7413 |
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課程識別碼 |
221 U3950 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三6(13:20~14:10)星期四7,8(14:20~16:20) |
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上課地點 |
天數201天數201 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1002npde |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
In this semester, we will begin by introducing finite volume methods for
solving hyperbolic problems, and then talk a little bit about finite element methods before moving to the discussion of discontinuous Galerkin method for
approximating various types of PDEs. |
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課程目標 |
... |
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課程要求 |
Explore existing public scientific software such as Chombo, FronTier, Clawpack,
Geoclaw, Oversets, and many others for real computations |
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預期每週課後學習時數 |
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Office Hours |
每週三 11:00~12:00 |
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指定閱讀 |
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參考書目 |
1. R.J. LeVeque, Numerical methods for conservation laws, Birkhauser 1992
2. R.J. LeVeque, Finite volume methods for hyperbolic problems, Cambridge, 2002
3. J.S. Hesthaven and T. Warburton, Nodal discontinuous Galerkin methods,
Algorithms, Analysis, and Applications, Springer 2008,
4. B. Riviere, Discontinuous Galerkin methods for solving elliptic and parabolic
equations: Theory and Implementation, SIAM, 2008 |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Project/Presentation |
60% |
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2. |
Assignments |
40% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/22,2/23 |
Course overview |
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第2週 |
2/29,3/01 |
Conservative finite-volume method |
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第3週 |
3/07,3/08 |
No class (attend a conference abroad) |
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第4週 |
3/14,3/15 |
Lax-Wendroff theorem
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第5週 |
3/21,3/22 |
Entropy inequalities & Godunov's method |
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第6週 |
3/28,3/29 |
Entropy consistent Godunov's solution & Riemann problem for p-system |
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第8週 |
4/11,4/12 |
Hugoniot locus & integral curves |
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第9週 |
4/18,4/19 |
Riemann problem for p-system |
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第10週 |
4/25,4/26 |
Roe linearization |
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第11週 |
5/02,5/03 |
Path-conservative schemes |
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第12週 |
5/09,5/10 |
relaxation scheme |
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第13週 |
5/16,5/17 |
Asymptotic-preserving relaxation scheme |
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第14週 |
5/23,5/24 |
Discontinuous Galerkin (DG) method |
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第15週 |
5/30,5/31 |
DG (cont) |
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第16週 |
6/06,6/07 |
DG (cont) |
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